This material has been published in J. Difference Equ. Appl. 5 (1999), 335-351, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Taylor & Francis. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

A new proof of the M-R-R conjecture - including a generalization

(13 pages)

Abstract. We evaluate the determinant $\det_{0\le i,j\le n-1}(\de_{ij}+\sum _{t,k=0} ^{n-1}\binom {i+\mu}t\binom {k+\nu}{k-t}\binom {j-k+\mu-1}{j-k} 2^{k-t})$ which gives the 2-enumeration of certain shifted plane partitions. This generalizes a result of Andrews (Aequationes Math. 33 (1987), 230-250), who evaluated this determinant for \nu=0, thereby proving a conjecture of Mills, Robbins and Rumsey (Discrete Math. 67 (1987), 43-55).

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